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JEE Main202311 Apr 2023Evening ShiftMathematicsSequences and SeriesActual

Let a , b , c and d be positive real numbers such that a + b + c + d = 11 . If the maximum value of a 5 b 3 c 2 d is 3750 β , then the value of β is

Options

  1. A90
  2. B110
  3. C55
  4. D108

Correct answer

A. 90

Step-by-step solution

Given: a + b + c + d = 11 We know that, AM ≥ GM ⇒ a 5 + a 5 + a 5 + a 5 + a 5 + b 3 + b 3 + b 3 + c 2 + c 2 + d 1 11 ≥ a 5 b 3 c 2 d 5 5 3 3 2 2 11 ⇒ a + b + c + d 11 ≥ a 5 b 3 c 2 d 5 5 3 3 2 2 11 ⇒ 11 11 ≥ a 5 b 3 c 2 d 5 5 3 3 2 2 11 ⇒ a 5 b 3 c 2 d 5 5 3 3 2 2 11 ≤ 1 ⇒ a 5 b 3 c 2 d ≤ 5 5 3 3 2 2 ⇒ a 5 b 3 c 2 d ≤ 90 · 3750 So, β = 90

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